Nope, we don't have one of those, but we do have an IRC chatroom. But be warned, the locals can be hostile, unresponsive and of old age.
Personally I find a chatbox a little redundant, since we have so many other ways of communicating around these parts with irc chat, PM/visitor messages and our always casual General Chat. Our server isn't very stable either, not sure how much worse a chatbox would make it.
In conclusion: I don't know anything about servers and bandwidth and I'm kinda hungry, I think I'm going to eat a ham and cheese pie.